Class 11 Mathematics Chapter 2 – Matrices and Determinants MCQs | FBISE | Grade 11 Math - MCQs

Practice 50 exam-oriented MCQs covering matrices, matrix operations, determinants, inverse matrices and related concepts for FBISE HSSC-I Mathematics.

1. A matrix is a rectangular arrangement of numbers or elements in:

A) Rows and columns
B) Lines and angles
C) Sets only
D) Fractions only

2. The order of a matrix having 3 rows and 4 columns is:

A) 4 × 3
B) 3 × 4
C) 7 × 1
D) 12 × 1

3. A matrix having the same number of rows and columns is called a:

A) Row matrix
B) Column matrix
C) Square matrix
D) Rectangular matrix

4. A matrix with only one row is called a:

A) Column matrix
B) Row matrix
C) Square matrix
D) Null matrix

5. A matrix with only one column is called a:

A) Row matrix
B) Column matrix
C) Scalar matrix
D) Diagonal matrix

6. A matrix of order 2 × 3 contains:

A) 5 elements
B) 6 elements
C) 8 elements
D) 9 elements

7. Two matrices are equal if they have the same order and their corresponding elements are:

A) Different
B) Reciprocal
C) Equal
D) Negative

8. A matrix in which every element is zero is called a:

A) Identity matrix
B) Scalar matrix
C) Zero matrix
D) Unit matrix

9. The identity matrix of order 2 is:

A) [[1,1],[1,1]]
B) [[0,1],[1,0]]
C) [[1,0],[0,1]]
D) [[0,0],[0,0]]

10. In a square matrix, the entries from the upper-left corner to the lower-right corner form the:

A) Secondary diagonal
B) Principal diagonal
C) Row diagonal
D) Column diagonal

11. A diagonal matrix has all its elements outside the principal diagonal equal to:

A) 1
B) −1
C) Zero
D) Any non-zero number

12. A scalar matrix is a diagonal matrix in which all diagonal elements are:

A) Equal
B) Zero
C) Different
D) Negative

13. The transpose of a matrix is obtained by interchanging its:

A) Elements and signs
B) Rows and columns
C) Diagonal elements
D) Determinants

14. If A is a 2 × 3 matrix, then the order of Aᵀ is:

A) 2 × 3
B) 3 × 2
C) 2 × 2
D) 3 × 3

15. A square matrix A is symmetric if:

A) Aᵀ = A
B) Aᵀ = −A
C) A = 0
D) A² = A

16. A square matrix A is skew-symmetric if:

A) Aᵀ = A
B) Aᵀ = −A
C) Aᵀ = I
D) A = I

17. The diagonal elements of a skew-symmetric matrix are always:

A) 1
B) −1
C) Zero
D) Equal to each other

18. Two matrices can be added only when they have:

A) The same determinant
B) The same order
C) The same diagonal
D) The same number of zeros

19. If A and B are conformable for addition, then A + B is obtained by:

A) Multiplying corresponding elements
B) Adding corresponding elements
C) Dividing corresponding elements
D) Transposing both matrices

20. Matrix addition is:

A) Commutative
B) Never commutative
C) Defined only for square matrices
D) Always equal to multiplication

21. The additive identity for matrices is the:

A) Identity matrix
B) Zero matrix
C) Scalar matrix
D) Transpose matrix

22. The additive inverse of a matrix A is:

A) A
B) A²
C) −A
D) A⁻¹

23. If A is a matrix, then A + (−A) equals:

A) A
B) −A
C) I
D) Zero matrix

24. Multiplication of a matrix by a scalar means multiplying:

A) Only diagonal elements
B) Every element by the scalar
C) Only non-zero elements
D) Only the first row

25. If A is of order 2 × 3 and B is of order 3 × 4, then AB has order:

A) 2 × 4
B) 3 × 3
C) 4 × 2
D) 2 × 3

26. For the product AB to be defined, the number of columns of A must equal the number of:

A) Rows of A
B) Columns of B
C) Rows of B
D) Elements of B

27. In general, matrix multiplication is:

A) Commutative
B) Not commutative
C) Impossible
D) Always scalar

28. If AB is defined, the element in row i and column j of AB is obtained by:

A) Adding all elements of A and B
B) Taking the dot product of row i of A with column j of B
C) Subtracting corresponding elements
D) Multiplying only diagonal elements

29. Matrix multiplication is associative, so for conformable matrices:

A) A(BC) = (AB)C
B) A(BC) = AB + C
C) A(BC) = A + BC
D) A(BC) = ABCᵀ

30. The distributive law for matrices includes:

A) A(B + C) = AB + AC
B) A(B + C) = AB + BC
C) A(B + C) = A + B + C
D) A(B + C) = BA + CA

31. The determinant of a 2 × 2 matrix $\begin{pmatrix}a&b\\c&d\end{pmatrix}$ is:

A) ad + bc
B) ab − cd
C) ad − bc
D) ac − bd

32. The determinant of $\begin{pmatrix}2&3\\1&4\end{pmatrix}$ is:

A) 5
B) 8
C) 11
D) −5

33. A determinant is defined for:

A) Any rectangular matrix
B) Square matrices
C) Row matrices only
D) Column matrices only

34. If the two rows of a determinant are identical, its value is:

A) 1
B) −1
C) 0
D) 2

35. If two rows of a determinant are interchanged, the determinant:

A) Remains unchanged
B) Becomes its negative
C) Becomes zero always
D) Is squared

36. If all elements of one row of a determinant are multiplied by k, the determinant is multiplied by:

A) k
B) k²
C) 1/k
D) k + 1

37. The determinant of an identity matrix of any order is:

A) 0
B) 1
C) −1
D) Equal to its order

38. The determinant of a triangular matrix is equal to the:

A) Sum of all elements
B) Product of its diagonal elements
C) Product of off-diagonal elements
D) Square of its order

39. A square matrix A is singular if:

A) |A| = 1
B) |A| = −1
C) |A| = 0
D) A = I

40. A square matrix A is non-singular if:

A) |A| = 0
B) |A| ≠ 0
C) A has no rows
D) A is a zero matrix

41. If A is a 2 × 2 matrix, then an inverse A⁻¹ exists when:

A) |A| = 0
B) |A| ≠ 0
C) A has equal rows
D) A is rectangular

42. For a non-singular square matrix A, the product AA⁻¹ is:

A) A
B) 0
C) I
D) −I

43. The inverse of a 2 × 2 matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$ , when $ad-bc\neq0$ , is:

A) $\frac{1}{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}$
B) $\frac{1}{ad+bc}\begin{pmatrix}a&b\\c&d\end{pmatrix}$
C) $\begin{pmatrix}d&b\\c&a\end{pmatrix}$
D) $\frac{1}{ad-bc}\begin{pmatrix}a&-c\\-b&d\end{pmatrix}$

44. The determinant of $\begin{pmatrix}1&2\\3&4\end{pmatrix}$ is:

A) −2
B) 2
C) 10
D) −10

45. If $A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$ , then $A^T$ is:

A) $\begin{pmatrix}1&2\\3&4\end{pmatrix}$
B) $\begin{pmatrix}1&3\\2&4\end{pmatrix}$
C) $\begin{pmatrix}4&3\\2&1\end{pmatrix}$
D) $\begin{pmatrix}2&1\\4&3\end{pmatrix}$

46. If $A=\begin{pmatrix}1&0\\0&1\end{pmatrix}$ , then A is:

A) Zero matrix
B) Identity matrix
C) Row matrix
D) Skew-symmetric matrix

47. If A and B are matrices of the same order, then $(A+B)^T$ equals:

A) $A^T+B^T$
B) $A^T-B^T$
C) $AB$
D) $BA$

48. If $A=\begin{pmatrix}2&0\\0&2\end{pmatrix}$ , A is a:

A) Scalar matrix
B) Row matrix
C) Skew-symmetric matrix
D) Zero matrix

49. The determinant of a matrix with a row of all zeros is:

A) 1
B) −1
C) 0
D) Undefined

50. If $|A|=3$ for a non-singular square matrix A, then $|A^{-1}|$ is:

A) 3
B) −3
C) $\frac{1}{3}$
D) 0

Explore More Class 11 Mathematics MCQs

Chapter 1 – Complex Numbers
Chapter 2 – Matrices and Determinants
Chapter 3 – Vectors
Chapter 4 – Sequences and Series
Chapter 5 – Polynomials
Chapter 6 – Permutation and Combination
Chapter 7 – Mathematical Induction and Binomial Theorem
Chapter 8 – Fundamentals of Trigonometry
Chapter 9 – Trigonometric Functions

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These MCQs are designed around the chapter’s core matrices and determinants concepts: matrix formation and order, equality and types of matrices, transpose, symmetric and skew-symmetric matrices, addition and scalar multiplication, matrix multiplication and its laws, determinants, determinant properties, singular and non-singular matrices, and inverse matrices. The questions emphasize knowledge, understanding and application-oriented practice suitable for FBISE-style preparation.

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